# Percentage Difference, Percentage Error, Percentage Change

They are very similar ...

They all show a difference between two values as a percentage of one (or both) values

• Use Percentage Change when comparing an Old Value to a New Value
• Use Percentage Error when comparing an Approximate Value to an Exact Value
• Use Percentage Difference when both values mean the same kind of thing (one value is not obviously older or better than the other).

(Refer to those links for more details)

## How to Calculate

Step 1: Subtract one value from the other

Step 2: Then divide by ... what?

• Percentage Change: Divide by the Old Value
• Percentage Error: Divide by the Exact Value
• Percentage Difference: Divide by the Average of The Two Values

Step 3: Is the answer negative?

• Percentage Change: a positive value is an increase, a negative value is a decrease.
• Percentage Error: ignore a minus sign (just leave it off), unless you want to know if the error is under or over the exact value
• Percentage Difference: ignore a minus sign, because neither value is more important, so being "above" or "below" does not make sense.

Step 4: Convert this into a percentage (multiply by 100 and add a % sign)

## The Formulas

(Note: the "|" symbols mean absolute value, so negatives become positive.)

Percent Change = New Value − Old Value|Old Value| × 100%

### Example: There were 200 customers yesterday, and 240 today:

240 − 200|200|× 100% = 40200 × 100% = 20%

A 20% increase.

Percent Error = |Approximate Value − Exact Value||Exact Value| × 100%

### Example: I thought 70 people would turn up to the concert, but in fact 80 did!

|70 − 80||80| × 100% = 1080 × 100% = 12.5%

I was in error by 12.5%

(Without using the absolute value, the error is −12.5%, meaning I under-estimated the value)

Percentage Difference = |First Value − Second Value(First Value + Second Value)/2| × 100%

### Example: "Best Shoes" gets 200 customers, and "Cheap Shoes" gets 240 customers:

|240 − 200(200+240)/2| × 100% = |40220| × 100% = 18.18...%

Rounded off, that is an 18% difference between them.